Sentence examples for mathematical properties including from inspiring English sources

We provide a comprehensive treatment of its general mathematical properties including quantile and generating functions, ordinary and incomplete moments and other properties.

In "Properties of the new model" section, we obtain some of its mathematical properties including quantile function (qf), tail behaviors, a useful linear representation for its density function and some types of moments.

These mathematical properties include Bayes estimators and posterior risks for the unknown component and proportion parameters using the non-informative and the informative priors under squared error loss function, precautionary loss function and DeGroot loss function.

Course themes may include: mathematical properties of statistics used in human population genetics, mathematics of evolutionary trees, and the intersection of population genetics and phylogenetics.

We describe the mathematical properties of the new framework, including goodness-of-fit and identification and we illustrate how to apply the framework with three empirical examples.

The current paper is devoted to the study of the mathematical properties of this new model, including issues related to the existence and uniqueness of the minimizer, and its computational approach.

We first establish some important mathematical properties for the function ϕ in the model including the lower semicontinuity, the differential property, the convergence and regularization of its mollification ϕ ϵ.

These optimizations include the use of GPU acceleration and the exploitation of the mathematical properties of spherical harmonics, which are used as test functions in the moment formulation.

This training process is not a trivial task owing to factors including experimental error, limitations in the amount of data available, incompleteness of our prior knowledge and inherent mathematical properties of the models.

Mathematical programming includes the study of the mathematical structure of optimization problems, the invention of methods for solving these problems, the study of the mathematical properties of these methods, and the implementation of these methods on computers.

Programs without data structures may suffice for exploring mathematical properties.